Electric field for radially polarized coil

A while back, I created a document describing how one could create a radially polarized electromagnet (like a doughnut with the North pole in the center and the south pole on the outer edge) and I would like to know what the e-field would look like when the current is increasing in the coil.

It is easy to visualize the E field for a cylindrical coil with a changing magnet field but I'm having a hard time visualizing the vectors for the radial coil. In case this helps, I have attached the article I made about the coils.